REAL-ADHERE · Grant No. 101285102 · SURFACE · Grant No. 101039198 · Horizon Europe
An interactive, browser-based scientific demonstrator for exploring the force response of a rigid sphere in adhesive contact with a linear viscoelastic substrate under a loading–dwell–unloading protocol.
This demonstrator accompanies the study
Deep learning-based prediction of time-resolved adhesive forces in viscoelastic Hertzian contacts
a TriboDynamics Lab, Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Via Orabona 4, Bari 70125, Italy
b Chair of Cyber-Physical Systems in Mechanical Engineering, Technische Universität Berlin, Straße des 17. Juni, Berlin 10623, Germany
01 · Physical system
The physical problem is the axisymmetric adhesive contact between a rigid sphere and a linear-viscoelastic half-space. A finite-range Lennard–Jones traction–separation law acts across the evolving gap, while viscoelastic memory makes the normal force depend on the complete prescribed displacement history rather than on the instantaneous indentation alone. The loading–dwell–unloading protocol therefore couples approach, relaxation at fixed indentation, and detachment; its force trajectory is governed jointly by the loading and unloading rates, dwell time, peak indentation, adhesion range, and contact modulus.
02 · Dimensionless formulation
Dimensionless variables remove the particular unit scale, allowing the surrogate to represent systems that share the same reduced physics.
τr is the viscoelastic relaxation time; hats denote dimensionless quantities.
μ is the dimensionless Tabor parameter controlling the transition from long-range/DMT-like to short-range/JKR-like adhesion.
R is sphere radius, Δγ0 thermodynamic surface energy, h0 interaction range, and E* contact modulus.
03 · Interactive M1-concat surrogate
Enter the five parameters in the order reported in Table 1. The defaults reproduce sample 11. Prediction runs entirely on your device; values are never uploaded or stored.
Support score will appear after prediction.
Out-of-distribution prediction — the surrogate has not been validated in this region.
120 measurement steps with phase-resolved support
Enter a protocol and select Predict.
Actual M1-concat architecture
Figure 6-style force–indentation trajectory
The Figure 6-style prediction will appear here.
04 · Model provenance
The published bundle contains the original HDF5 model, its TensorFlow.js conversion, exact preprocessing scalers, and browser-safe support metadata. It does not contain raw training force trajectories.
05 · Scientific foundations
This demonstrator builds on the theoretical, numerical, and machine-learning studies listed below. If you use its scientific ideas, model, data, or visualisations in scholarly work, please cite the relevant publications in addition to this demonstrator.